## Mathematics 255A F06, Lecture 1

Functional Analysis

E. Effros

## MS 5148, MWF 10-10:50

If you are not a registered in this
course, please send me your email address. It is likely that I will be
sendng out further information by course email.

**Instructor Information**
- Office Location: MS 6931
- Office Hours: Monday 4-5

- Email Address: ege@math.ucla.edu

Syllabus: We will cover the
following topics

- the spectral theorem for bounded normal operators on a Hilbert
space, together with a discussion of how operators are used in quantum
mechanics (you won't need to know any
physics for this)

- the Gelfand-Naimark theorem characterizing C*-algebras
- compact operators on Banach spaces and on Hilbert spaces
- Fredholm operators and some of their applications
- various topics from quantized mathematics (time permitting)

Text:
[C] Conway, A course in
Functional analysis: We will use this as a source of homework problems
and a place to look up some of the details that I will not cover in
lecture.

Grades: Grades
will be in the A-B range, and will depend upon homework
assignments.

Assignment 1: [C] page 36: 1, 2, 5, 6, 9, 11.

Assignment 2: page 243: 5 - 11, 13 (for
counter-examples it often suffices to consider 2x2 matrices), 14.